It is desirable in many applications to extract or separate independent signal components from a signal mixture, such as a electronic (e.g., digital) signal mixture. For example, in imaging, it is highly useful to separate physiologic signal on dynamic medical image data to obtain images with improved demarcations. Other nonlimiting example applications include extraction of a source signal from a multispectral image, extracting signal data from sensor array signal data, separation of mixed digitized audio signals, etc.
It may be desirable to separate signals on either a spatial or a temporal basis. Independent Component Analysis (ICA) is a method for such temporal and spatial signal extractions. The general form of the ICA method is described in Eq. (1) below, where X is the signal mixture array (matrix), W is the unmixing (weight) matrix, and S is the estimated source signal array (matrix).S=WX  (1)
The transformation of X by W is a matrix multiplication, which is the inner product of row vectors in W with column vectors in X. Graphically, this is the projection of X onto W. Example ICA methods in the art include AMUSE, JADE, SOBI, and FastICA.
To estimate an optimal unmixing matrix for ICA, many prior methods for ICA involve a further transformation of S by g(S) based on a model probability density function (pdf) or a model cumulative density function (cdf) of the source signal. In such methods, there is a search for an unmixing matrix W that maximizes the entropy of the system (e.g., Infomax method) or maximizes the likelihood estimate to a given model (e.g., Maximum Likelihood method). The actual probability density function of the source signal is not known. However, these techniques work if the model probability density functions are an approximation to the source signal probability density functions.